Structure of the antiproton-proton elastic scattering amplitude

It is found that the simple expression $[(\pi cq)/{\rm sh}(\pi cq)][J_1(Rq)/(Rq)]$ for the elastic scattering amplitude makes it possible to well describe differential cross sections over a broad range of energies from 100 MeV to $\sqrt{s}=1800$ GeV. This parametrization can be used to calculate antiproton-nucleus and antinucleus-nucleus amplitudes and cross sections, which are necessary in accelerator experiments and in cosmic ray physics. The generalization of the wavelet expansion to the case of functions defined on a semi-infinite interval is also proposed.